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Crystal graphs of higher level q-deformed Fock spaces, Lusztig a-values and Ariki-Koike algebras

Nicolas Jacon
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Abstract

We show that the different labelings of the crystal graph for irreducible highest weight $\mathcal{U}\_q (\hat{\mathfrak{sl}}\_e)$-modules lead to different labelings of the simple modules for non semisimple Ariki-Koike algebras by using Lusztig $a$-values.

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BibTeXRIS

Nicolas Jacon. 2006-03-13. Crystal graphs of higher level q-deformed Fock spaces, Lusztig a-values and Ariki-Koike algebras. https://arxiv.org/abs/math/0504267

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